Preheat oven to 450 degrees.

Separate garlic cloves, leaving skins intact, and wrap together in foil.

Bake garlic in upper third of oven for 1 hour.

Quarter bell pepper lengthwise and discard stems, seeds, and ribs.

Arrange pepper quarters skin side up in a shallow baking pan.

Roast peppers for 20 minutes.

Cool peppers, then peel and transfer to a blender.

Remove garlic from foil and squeeze pulp into blender.

Trim fennel stalks flush with bulbs and discard any tough outer layers.

Cut fennel bulbs lengthwise into 1/8-inch-thick slices.

Halve fennel slices lengthwise, if desired.

Transfer fennel to a bowl of ice and cold water.

Chill fennel at least 30 minutes, or until crisp, and up to 3 hours.

Dry-roast cumin and caraway seeds in a small heavy skillet over moderate heat, stirring, until fragrant and a few shades darker, about 1 minute.

Grind seeds to a powder in a cleaned electric coffee grinder.

Add ground seeds and remaining dip ingredients to pepper mixture.

Puree mixture until smooth.

Dip may be made 5 days ahead and chilled, covered.

Drain fennel in a colander and pat dry.

Serve dip with fennel.